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摘要: 给出了由高斯径向基函数生成的一组小波框架,建立在小波框架理论的基础上,构造 性地证明了高斯径向基函数网络可以任意精度地逼近L2(Rd)中的函数.在此基础上,利用高斯 径向基函数的时频局部化性质和自适应投影原理,进一步给出了构造和训练网络的自适应学习 算法.应用到信号的重构和去噪,获得了良好的效果.Abstract: A set of wavelet frames generated by Gaussian radial basis functions are presented. It is constructively proved that a radial basis function network with Gaussian activation functions can approximate any function in L2 (Rd) with desired accuracy. Furthermore, an adaptive learning algorithm for constructing and training networks is proposed based on time-frequency localization properties of Gaussian radial basis functions and the adaptive projection algorithm. Applications to signal reconstruction and noise elimination are given.
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